Joint Colloquium: Hytoenen -- How to choose random cubes, and why?

___________________JOINT COLLOQUIUM______________________ 

Speaker: Prof.  Tuomas Hytönen, (University of Helsinki) 

Title: How to choose random cubes, and why? 

Date: Friday, August 7, 2009 Time: 2:00 pm Venue: Room 275 Carslaw Building, University
of Sydney 

Abstract: 

 A standard tool in mathematical analysis is the refining sequence of partitions of the
Euclidean space into cubes with side-lengths equal to powers of two, the so-called
dyadic cubes.  Associated to the system of dyadic cubes, there is a natural basis of
square-integrable functions, the Haar system, which has proven useful e.g.  in the
analysis of singular integral operators.  In their work on singular integrals related to
quite general measures, Nazarov, Treil and Volberg observed that, while certain matrix
coefficients of such an operator with respect to the Haar basis do not admit any good
control, such bad situations only occur "rarely", which can be made precise in the sense
of probability by working with a randomly chosen dyadic system, instead of a fixed one.
I will discuss how these random cubes a chosen in the original Euclidean framework, and
also what they could be in a more general metric space.  

 The Speaker will have been taken to lunch at the University of New South Wales before
the colloquium.